The advancement of Artificial Intelligence (AI) has catalyzed revolutionary changes across various sectors, notably in healthcare. Among the significant developments in this field are the applications of generative AI models, specifically transformers and diffusion models. These models have played a crucial role in analyzing diverse forms of data, including medical imaging (encompassing image reconstruction, image-to-image translation, image generation, and image classification), protein structure prediction, clinical documentation, diagnostic assistance, radiology interpretation, clinical decision support, medical coding, and billing, as well as drug design and molecular representation. Such applications have enhanced clinical diagnosis, data reconstruction, and drug synthesis. This review paper aims to offer a thorough overview of the generative AI applications in healthcare, focusing on transformers and diffusion models. Additionally, we propose potential directions for future research to tackle the existing limitations and meet the evolving demands of the healthcare sector. Intended to serve as a comprehensive guide for researchers and practitioners interested in the healthcare applications of generative AI, this review provides valuable insights into the current state of the art, challenges faced, and prospective future directions.